Confused on how to do the Definition of A Derivative.

Confused on how to do the Definition of A Derivative.

I have a problem on limits. The graph shows two very different equations approaching the same point, but at that point (x=4) there is a hole. Below the hole there is a point at (4,2). What is the...

Find the indicated limit, if it exists. (If an answer does not exist, enter DNE.) lim (x->infinity) ((24 x^4 - x^3 + x + 8)/(8 x^4 + 2 x^3 + x^2 +...

How do I go about proving limits for given sequences and series, for example how would i prove that the limit when x tends to infinity of n^(1/n)=1?

Find the limit as x goes to 0: (ln(1+x2)-x(arctan(x)))/(x(sin(x)-x)) At first the fraction found is 0/0, but applying L'Hopitals rule, when differentiated...

To solve a limit as x is approaching 0 while the function is x / (sin3x), what is the step by step process...? I've seen many sites online that go through this problem, yet is completely confusing...

lim x->-pi/2 (1+ cos (2x))/(2x+ pi )^2

This is what I have so far: Limx-->∞ 1/(x^4+x^2+5)=0 if for all ϵ>0 we find a value x_c depending on ϵ such that | 1/(x^4+x^2+5)|< ϵ I...

an=e(-1/sqrt(n)) Apparently in converges and the limit is 1 but I'm not really sure how to do this type of problem with a limit of ex {n2e-n} Limit converges to 0? How?...

(tanx/7)/(2x-pi)

Hello. I’ve spent more than half an hour at this point trying to prove that limit as x and y got to 1 and 2 for function (x-1)((y-2)^2)/(((x-1)^2)+((y-2)^2)) is zero. Do you know how to prove...

So the limit as n=> 0+ for abs(X^2 - x/100)/(x^2 - x/100) = -1, NOT 1, as I initially thought. My logic in getting 1 was that plugging in small integral values > 0 (since...

Find multivariable limits and explain lim (x,y) -> (0,0) = (x^4-y^4)/(x^2+y^2) lim (x,y) -> (0,0) = xy/sqrt(x^2+y^2)

a) if limit of f(x) as x approaches a exists, then limit of |f(x)| as x approaches a exists. is this true or false? why or why not? b) if limit of |f(x)| as x approaches...

find all horizontal and vertical asymptotes of y=x/sinx vertical asymptotes: if i set denominator to 0, then sinx=0 and x= 0 or npi? horizontal asymptotes:...

a) If lim f(x) exists, them lim |f(x)| exists x>a x>a b)...

With steps please using the epsilom-delta definition

The question follows: We model the pizza contained in the unit square S = {(x,y) : 0<=x,y<=1}. Prove that the function f(z) is continous on its domain which is [0,1]. by using eplison - delta...

Any hints on how to prove this? What can we use a a proper subsequence, knowing that a proper subsequence is any subsequence except for the sequence it self.

limx-->infinity (square root(9x2+x) - 3x)

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